Generalized log-logistic proportional hazard model: a non-penalty shrinkage approach
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Bibliographic record
Abstract
This paper considers the pretest and shrinkage estimation methods for estimating regression parameters of the generalized log-logistic proportional hazard (PH) model. This model is a simple extension of the log-logistic model, which is closed under the PH relationship. The generalized log-logistic PH model also has attributes similar to those of the Weibull model. We consider this model for right-censored data when some parameters shrink to a restricted subspace. This subspace information on the parameters is used to shrink the unrestricted model estimates toward the restricted model estimates. We then optimally combine the unrestricted and restricted estimates in order to define pretest and shrinkage estimators. Although this estimation procedure may increase bias, it also reduces the overall mean squared error. The efficacy of the proposed model and estimation techniques are shown using a simulation study as well as an application to real data. We also compare the performance of generalized log-logistic, Weibull, and Cox PH models for unimodal and increasing hazards. The shrinkage estimator poses less risk than the maximum likelihood estimator when the shrinkage dimension exceeds two; this is shown through simulation and real data applications.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it